Matrix multiplication is an important operation for many engineering applications. Sometimes new features that include matrix multiplication should be added to existing and even out-of-date embedded platforms. In this paper, an unusual problem is considered: how to implement matrix multiplication of 32-bit signed integers and fixed-point numbers on DSP having SIMD instructions for 16-bit integers only. For examined tasks, matrix size may vary from several tens to two hundred. The proposed mathematical approach for dense rectangular matrix multiplication of 32-bit numbers comprises decomposition of 32-bit matrices to matrices of 16-bit numbers, four matrix multiplications of 16-bit unsigned integers via outer product, and correction of outcome for signed integers and fixed point numbers. Several tricks for performance optimization are analyzed. In addition, ways for block-wise and parallel implementations are described. An implementation of the proposed method by means of 16-bit vector instructions is faster than matrix multiplication using 32-bit scalar instructions and demonstrates performance close to a theoretically achievable limit. The described technique can be generalized for matrix multiplication of n-bit integers and fixed point numbers via handling with matrices of n/2-bit integers. In conclusion, recommendations for practitioners who work on implementation of matrix multiplication for various DSP are presented.

Watershed is a widely used image segmentation algorithm. Most researchers understand just an idea of this method: a grayscale image is considered as topographic relief, which is flooded from initial basins. However, frequently they are not aware of the options of the algorithm and the peculiarities of its realizations. There are many watershed implementations in software packages and products. Even if these packages are based on the identical algorithm–watershed, by flooding their outcomes, processing speed, and consumed memory, vary greatly. In particular, the difference among various implementations is noticeable for huge volumetric images; for instance, tomographic 3D images, for which low performance and high memory requirements of watershed might be bottlenecks. In our review, we discuss the peculiarities of algorithms with and without waterline generation, the impact of connectivity type and relief quantization level on the result, approaches for parallelization, as well as other method options. We present detailed benchmarking of seven open-source and three commercial software implementations of marker-controlled watershed for semantic or instance segmentation. We compare those software packages for one synthetic and two natural volumetric images. The aim of the review is to provide information and advice for practitioners to select the appropriate version of watershed for their problem solving. In addition, we forecast future directions of software development for 3D image segmentation by watershed.

Ring artifacts are typical defects of computed tomography (CT) that degrade the quality of a 3D reconstructed image. Existing techniques for a ring reduction have various shortcomings and limitations, in particular, a lot of them are unable to process arbitrary fragments of the image and blur artifact-free regions. We propose an algorithm for ring artifacts segmentation and reduction by deep convolutional neural networks that correct 3D fragments of the CT image by inpainting. We compare 2D and 3D architectures of networks. For the creation of a dataset with a big number of ring artifacts, we propose a procedure that is able to transfer an artifact from one image to an arbitrary place of another image. The appearance of the transferred artifact changes. For ring artifact segmentation and correction in images of sandstones and sand, the proposed networks demonstrate good visual results and outperform existing methods. The proposed technique concentrates on the Digital Rock workflow, but the networks can be adjusted for the processing of other CT images as well.

Interfacial tension (IFT) is one of the key parameters governing multiphase flow in reservoir. One of standard IFT measurement techniques is pendant drop shape analysis, which includes an acquisition of the drop snapshots in visible light. Hence, the method is limited by optical transparency of an external fluid. Here we present a new approach, which is free from this limitation. It uses X-rays as an illumination source and provides a number of advantages and additional opportunities in the study of fluid interface behavior. Proposed method includes a drop generation inside a uniquely designed X-ray transparent cell for high pressure and temperature (HPHT) measurements placed inside an X-ray scanner and imaging of its evolution with time till equilibrium state. Since X-ray images significantly differ from the classical optical ones, a novel algorithm was developed for accurate drop shape detection and further mathematical processing for IFT value calculation. As a result, an IFT value evolution curve for a pair of fluids is obtained. Depending on relative densities of the fluids, different experimental schemes can be implemented: pendant or rising drop. The method was validated on various neat fluids with well-known IFT values and then was successfully applied for different real fluids systems. This work demonstrates the unique laboratory studies carried out on different liquid-fluid systems showing that the developed methodology works well at elevated pressure and temperature conditions. The developed method unlocks the possibility for an appropriate IFT measurements in surfactant-rich oil-water systems as well as in systems near the phase transition such as gas-condensates at a wide range of thermobaric reservoir conditions and increases feasibility of HPHT measurements due to simplification of the measuring system design.

Digital rock analysis is a prospective approach to estimate properties of oil and gas reservoirs. This concept implies constructing a 3D digital twin of a rock sample. Focused Ion Beam - Scanning Electron Microscope (FIB-SEM) allows to obtain a 3D image of a sample at nanoscale. One of the main specific features of FIB-SEM images in case of porous media is pore-back (or shine-through) effect. Since pores are transparent, their back side is visible in the current slice, whereas, in fact, it locates in the following ones. A precise segmentation of pores is a challenging problem. Absence of annotated ground truth complicates fine-tuning the algorithms for processing of FIB-SEM data and prevents successful application of machine- learning-based methods, which require a huge training set. Recently, several synthetic FIB- SEM images based on stochastic structures were created. However, those images strongly differ from images of real samples. We propose fast approaches to render semisynthetic FIB- SEM images, which imply that intensities of voxels of mineral matrix in a milling plane, as well as geometry of pore space, are borrowed from an image of rock sample saturated by epoxy. Intensities of voxels in pores depend on the distance from milling plane to the given voxel along a ray directed at an angle equal to the angle between FIB and SEM columns. The proposed method allows to create very realistic FIB-SEM images of rock samples with precise ground truth. Also, it opens the door for numerical estimation of plenty of algorithms for processing FIB-SEM data.

Ring artifacts in X-ray microtomographic images can lead to errors in the construction of digital twins of rock samples for flow simulation. Previously, we considered an algorithm for detecting ring artifacts by means of matching filtering of image slices in a polar coordinate system. However, that approach is inapplicable for an arbitrary fragment of an image and requires adjustment of parameters from image to image. In this paper, we propose the segmentation method based on convolutional neural network. Two network architectures are considered: SegNet and U-net. To create a big and representative training and validation datasets, we propose an algorithm for transferring ring artifacts detected by the existing approach from one image to another. Our task-specific data augmentation improves outcomes in comparison with conventional augmentation techniques. The trained model successfully segments ring artifacts even for sample images and artifacts that were not in the training set. The developed algorithm is used to assess the quality of microtomographic images and local correction of image regions damaged by ring artifacts.

Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) tomography provides a stack of images that represent serial slices of the sample. These images are displaced relatively to each other, and an alignment procedure is required. Traditional methods for alignment of a 3D image are based on a comparison of two adjacent slices. However, such algorithms are easily confused by anisotropy in the sample structure or even experiment geometry in the case of porous media. This may lead to significant distortions in the pore space geometry, if there are no stable fiducial marks in the frame. In this paper, we propose a new method, which meaningfully extends existing alignment procedures. Our technique allows the correction of random misalignments between slices and, at the same time, preserves the overall geometrical structure of the specimen. We consider displacements produced by existing alignment algorithms as a signal and decompose it into low and high-frequency components. Final transformations exclude slow variations and contain only high frequency variations that represent random shifts that need to be corrected. The proposed algorithm can operate with not only translations but also with arbitrary affine transformations. We demonstrate the performance of our approach on a synthetic dataset and two real FIB-SEM images of natural rock.

Ring artifacts are inevitable in microtomographic images. In a Digital Rock workflow, such defects might affect the subsequent segmentation and flow simulation. We propose a correction of ring artifacts in reconstructed microtomographic images by inpainting. Our blind inpainting method uses a 3D convolutional network U-net. For the creation of training and validation datasets, we suggest an algorithm for transferring real ring artifacts to an arbitrary place in the undistorted slices of 8 big images of sandstones and sand. The parameters of the deep neural network and loss functions are analyzed. A loss function based on the multi-scale structural similarity index (MS-SSIM) allows to achieve the best performance. The developed solution corrects ring artifacts perfectly from a point of view of visual assessment and outperforms existing inpainting methods according to quality metrics based on MS-SSIM and mean absolute error (MAE).

The paper considers a new algorithm for blind quality assessment of a slice of X-ray microtomographic image. We selected the following factors impacting on micro-CT image quality with respect to Digital Rock technology: smoothness, sharpness, contrast, absence of high-density regions and ring artifacts. We propose algorithms for estimation of partial quality measures for named factors inside Region-of-Interest, that is in area associated with a sample of rock or granular material. Total quality metrics is calculated as a product of these partial measures. Our method for quality assessment provides reasonable outcomes for synthetic and real slices of micro-CT images. We collected experts' judgments about quality of slices. Proposed solution has a high correlation with scores of experts and outperforms existing blind quality metrics. An application of developed method to all slices allows to obtain quality estimation for 3D micro-CT image.

We present an algorithm for processing of X-ray microtomographic (micro-CT) images that allows automatic selection of a sub-volume having the best visual quality for further mathematical simulation, for example, flow simulation. Frequently, an investigated sample occupies only a part of a volumetric image or the sample can be into a holder; a part of the image can be cropped. For each 2D slice across the Z-axis of an image, the proposed method locates a region corresponding to the sample. We explored applications of several existing blind quality measures for an estimation of the visual quality of a micro-CT image slice. Some of these metrics can be applied to ranking the image regions according to their quality. Our method searches for a cubic area located inside regions belonging to the sample and providing the maximal sum of the quality measures of slices crossing the cube across the Z-axis. The proposed technique was tested on synthetic and real micro-CT images of rocks.

Watershed is a widespread technique for image segmentation. Many researchers apply the method implemented in open source libraries without a deep understanding of its characteristics and limitations. In the review, we describe benchmarking outcomes of six open-source marker-controlled watershed implementations for the segmentation of 2D and 3D images. Even though the considered solutions are based on the same algorithm by flooding having O(n)computational complexity, these implementations have significantly different performance. In addition, building of watershed lines grows processing time. High memory consumption is one more bottleneck for dealing with huge volumetric images. Sometimes, the usage of more optimal software is capable of mitigating the issues with the long processing time and insufficient memory space. We assume parallel processing is capable of overcoming the current limitations. However, the development of concurrent approaches for the watershed segmentation remains a challenging problem.

Geomagnetic pulsations of the serpentine-emission (SE) type are considered. A method for estimating the frequency and amplitude parameters in the form of a time function for pulsations—SE and the accompanying spectral components—is suggested. An estimation algorithm is developed on the basis of local approximating polyharmonic models and weighted moving average filtration. Examples of the estimation of the frequency and amplitude parameters of SE pulsations are given. It is proposed that the procedure be used to calculate the estimation errors in SE pulsation frequency parameters and to choose the tuning parameters.

The problem of the algorithmic recognition of anomalous time intervals in the time series of the sea-level observations conducted by the Russian Tsunami Warning Survey (RTWS) is considered. The normal and anomalous sea-level observations are described. The polyharmonic models describing the sea-level fluctuations on the short time intervals are constructed, and sea-level forecasting based on these models is suggested. The algorithm for the recognition of anomalous time intervals is developed and its work is tested on the real RTWS data.